Finite Group Databasebeta

C2×C4×#13133225 #28247497

order13568
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×#13133225

Splittings

FittingC2×C4×M16×C53 ⋊ C2
SylowC53 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC2×C42C22×D53
commutatorC2×C53C23×C42
FrattiniC2×C4C24×D53
FittingC2×C4×M16×C53C2
socleC23×C53C23×C4
prime radicalC22×#11719945C22
cosocleC2×C4×C53C25
hypercenterC2×C4×M16D53
hypocenterC53C2×C4×#131
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6784

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1032973);